On the naturality of the Mathai-Quillen formula

We give an alternative proof for the Mathai-Quillen formula for a Thom form using its natural behaviour with respect to fiberwise integration. We also study this phenomenon in general context.Comment: 6 page

No four subsets forming an N

AbstractWe survey results concerning the maximum size of a family F of subsets of an n-element set such that a certain configuration is avoided. When F avoids a chain of size two, this is just Sperner's theorem. Here we give bounds on how large F can be such that no four distinct sets A,B,C,D∈F satisfy A⊂B, C⊂B, C⊂D. In this case, the maximum size satisfies (n⌊n2⌋)(1+1n+Ω(1n2))⩽|F|⩽(n⌊n2⌋)(1+2n+O(1n2)), which is very similar to the best-known bounds for the more restrictive problem of F avoiding three sets B,C,D such that C⊂B, C⊂D

Centrosymmetric graphs and a lower bound for graph energy of fullerenes

The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs

The Wahlquist metric cannot describe an isolated rotating body

It is proven that the Wahlquist perfect fluid space-time cannot be smoothly joined to an exterior asymptotically flat vacuum region. The proof uses a power series expansion in the angular velocity, to a precision of the second order. In this approximation, the Wahlquist metric is a special case of the rotating Whittaker space-time. The exterior vacuum domain is treated in a like manner. We compute the conditions of matching at the possible boundary surface in both the interior and the vacuum domain. The conditions for matching the induced metrics and the extrinsic curvatures are mutually contradictory.Comment: 13 pages, 0 figure

Density Functional Molecular Study on the Full Conformational Space of the S-4-(2-Hydroxypropoxy)carbazol Fragment of Carvedilol (1-(9H−Carbazol-4-yloxy)-3- [2-(2-methoxyphenoxy)ethylamino]-2-propanol) in Vacuum and in Different Solvent Media

Density functional theory (DFT) conformational analysis was carried out on the potential energy hypersurface (PEHS) of the carbazole-containing molecular fragment, S-4-(2-hydroxypropoxy)-carbazol, of the chiral cardiovascular drug molecule carvedilol, (1-(9H-carbazol-4-yloxy)-3-[2-(2-methoxy-phenoxy)ethylamino]-2-propanol) . The PEHS was computed in vacuum, chloroform, ethanol, DMSO, and water at the B3LYP/6-31G(d) level of theory. The carbazole ring system was confirmed to be planar, and the resultant PEHS in vacuum contained 19 converged minima, of which the global minima possessed a conformation with chi(1), chi(2), and chi(3) in the anti position and chi(10) in the g position. Conformer stability for the S-4-(2-hydroxypropoxy)carbazol PEHS was influenced by intramolecular hydrogen bonding. Tomasi PCM reaction-field calculations revealed that the lowest SCF energies, relative conformer energies, and solvation free energies (DeltaG (solvation)) for the S-4-(2-hydroxypropoxy)carbazol PEHS were in protic solvents, ethanol and water, because of the larger hydrogen bond donor values of these solvents, which aid in stabilization of the dipole moment created by the carbazole ring system and the oxygen and nitrogen atoms. However, solvent effects contributed most significantly to the stabilization of S-4-(2-hydroxypropoxy)carbazol conformers that contained no internal hydrogen bonding, whereas solvent effects were not as important for conformers that contained intramolecular hydrogen bonding

Detection of complete and partial chromosome gains and losses by comparative genomic in situ hybridization

Comparative genomic in situ hybridization (CGH) provides a new possibility for searching genomes for imbalanced genetic material. Labeled genomic test DNA, prepared from clinical or tumor specimens, is mixed with differently labeled control DNA prepared from cells with normal chromosome complements. The mixed probe is used for chromosomal in situ suppression (CISS) hybridization to normal metaphase spreads (CGH-metaphase spreads). Hybridized test and control DNA sequences are detected via different fluorochromes, e.g., fluorescein isothiocyanate (FITC) and tetraethylrhodamine isothiocyanate (TRITC). The ratios of FITC/TRITC fluorescence intensities for each chromosome or chromosome segment should then reflect its relative copy number in the test genome compared with the control genome, e.g., 0.5 for monosomies, 1 for disomies, 1.5 for trisomies, etc. Initially, model experiments were designed to test the accuracy of fluorescence ratio measurements on single chromosomes. DNAs from up to five human chromosome-specific plasmid libraries were labeled with biotin and digoxigenin in different hapten proportions. Probe mixtures were used for CISS hybridization to normal human metaphase spreads and detected with FITC and TRITC. An epifluorescence microscope equipped with a cooled charge coupled device (CCD) camera was used for image acquisition. Procedures for fluorescence ratio measurements were developed on the basis of commercial image analysis software. For hapten ratios 4/1, 1/1 and 1/4, fluorescence ratio values measured for individual chromosomes could be used as a single reliable parameter for chromosome identification. Our findings indicate (1) a tight correlation of fluorescence ratio values with hapten ratios, and (2) the potential of fluorescence ratio measurements for multiple color chromosome painting. Subsequently, genomic test DNAs, prepared from a patient with Down syndrome, from blood of a patient with Tcell prolymphocytic leukemia, and from cultured cells of a renal papillary carcinoma cell line, were applied in CGH experiments. As expected, significant differences in the fluorescence ratios could be measured for chromosome types present in different copy numbers in these test genomes, including a trisomy of chromosome 21, the smallest autosome of the human complement. In addition, chromosome material involved in partial gains and losses of the different tumors could be mapped to their normal chromosome counterparts in CGH-metaphase spreads. An alternative and simpler evaluation procedure based on visual inspection of CCD images of CGH-metaphase spreads also yielded consistent results from several independent observers. Pitfalls, methodological improvements, and potential applications of CGH analyses are discussed

Repetition Probability Does Not Affect fMRI Repetition Suppression for Objects

Previously several functional magnetic resonance imaging (fMRI) studies point toward the role of perceptual expectations in determining adaptation or repetition suppression (RS) in humans. These studies showed that the probability of repetitions of faces within a block influences the magnitude of adaptation in face-related areas of the human brain (Summerfield et al., 2008). However, a current macaque single-cell/local field potential (LFP) recording study using objects as stimuli found no evidence for the modulation of the neural response by the repetition probability in the inferior temporal cortex (Kaliukhovich and Vogels, 2010). Here we examined whether stimulus repetition probability affects fMRI repetition suppression for nonface object stimuli in the human brain. Subjects were exposed to either two identical [repetition trials (RTs)] or two different [alternation trials (ATs)] object stimuli. Both types of trials were presented blocks consisting of either 75% [repetition blocks (RBs)] or 25% [alternation blocks (ABs)] of RTs. We found strong RS, i.e., a lower signal for RTs compared to ATs, in the object sensitive lateral occipital cortex as well as in the face-sensitive occipital and fusiform face areas. More importantly, however, there was no significant difference in the magnitude of RS between RBs and ABs in each of the areas. This is in agreement with the previous monkey single-unit/LFP findings and suggests that RS in the case of nonface visual objects is not modulated by the repetition probability in humans. Our results imply that perceptual expectation effects vary for different visual stimulus categories